3 Description

F08GGF (DOPMTR) is intended to be used after a call to F08GEF (DSPTRD), which reduces a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation: A=QTQT. F08GEF (DSPTRD) represents the orthogonal matrix Q as a product of elementary reflectors.

This routine may be used to form one of the matrix products

QC,QTC,CQ​ or ​CQT,

overwriting the result on C (which may be any real rectangular matrix).

A common application of this routine is to transform a matrix Z of eigenvectors of T to the matrix QZ of eigenvectors of A.

9 Example

using packed storage. Here A is symmetric and must first be reduced to tridiagonal form T by F08GEF (DSPTRD). The program then calls F08JJF (DSTEBZ) to compute the requested eigenvalues and F08JKF (DSTEIN) to compute the associated eigenvectors of T. Finally F08GGF (DOPMTR) is called to transform the eigenvectors to those of A.